1. Pegasus Lectures, Inc. COPYRIGHT 2006 Volume I Companion Presentation Frank R. Miele Pegasus Lectures, Inc. Ultrasound Physics & Instrumentation 4 th Edition

2. Pegasus Lectures, Inc. COPYRIGHT 2006 License Agreement This presentation is the sole property of Pegasus Lectures, Inc. No part of this presentation may be copied or used for any purpose other than as part of the partnership program as described in the license agreement. Materials within this presentation may not be used in any part or form outside of the partnership program. Failure to follow the license agreement is a violation of Federal Copyright Law. All Copyright Laws Apply.

3. Pegasus Lectures, Inc. COPYRIGHT 2006 Volume I Outline  Chapter 1: Mathematics  Chapter 2: Waves  Level 1  Level 2  Chapter 3: Attenuation  Chapter 4: Pulsed Wave  Chapter 5: Transducers  Chapter 6: System Operation

4. Pegasus Lectures, Inc. COPYRIGHT 2006 Chapter 2: Waves - Level 1

5. Pegasus Lectures, Inc. COPYRIGHT 2006 Chapter 2: Waves Waves are a cyclical transfer of energy. Some wave examples:  water  sound  light  x-rays  radio signals

6. Pegasus Lectures, Inc. COPYRIGHT 2006 Waves can be classified many ways – one classification is based on whether or not the wave needs a medium to propagate. Sound is a mechanical wave. Wave Classifications WAVES Electromagnetic Mechanical Exist in a medium or vacuum Need a medium Fig. 1: (Pg 83)

7. Pegasus Lectures, Inc. COPYRIGHT 2006 Wave Propagation Classification Mechanical waves are further classified according to how they propagate. Fig. 2: (Pg 84)

8. Pegasus Lectures, Inc. COPYRIGHT 2006 Transverse Wave Propagation Fig. 3: Transverse Waves (Pg 85) Transverse waves propagate by particle motion that is perpendicular or “transverse” to the wave propagation direction.

9. Pegasus Lectures, Inc. COPYRIGHT 2006 Longitudinal Wave Propagation Fig. 4: (Pg 85) Longitudinal waves propagate by particle compression and rarefaction that results in particle motion that is “along” or in the same direction as the wave propagation direction.

10. Pegasus Lectures, Inc. COPYRIGHT 2006 Understanding “Static” Drawings Fig. 6: Case 1: Period = 2 seconds, Wavelength = 4 inches (Pg 87) Note that in a “static” drawing, the mNoteasurement of time and of distance appear as the same characteristic in the drawing.

11. Pegasus Lectures, Inc. COPYRIGHT 2006 Sound Wave Classification Fig. 5: (Pg 86) Sound is a longitudinal, mechanical wave.

12. Pegasus Lectures, Inc. COPYRIGHT 2006 Time versus Distance Fig. 7: Case 2: Period = 1 second, Wavelength = 4 inches (Pg 87) To correctly interpret whether time or distance is indicated in an image, you must pay attention to the labels on the graph.

13. Pegasus Lectures, Inc. COPYRIGHT 2006 Time versus Distance Fig. 8: Case 3: Period = 2 seconds, Wavelength = 6 inches (Pg 87) Note that in this case the period is 2 seconds (the time required to complete one cycle), whereas the wavelength is 6 inches (the distance from one wave peak to another wave peak).

14. Pegasus Lectures, Inc. COPYRIGHT 2006 Animation 1 of Time vs. Distance

15. Pegasus Lectures, Inc. COPYRIGHT 2006 Animation 2 of Time vs. Distance

16. Pegasus Lectures, Inc. COPYRIGHT 2006 Animation 3 of Time vs. Distance

17. Pegasus Lectures, Inc. COPYRIGHT 2006 Acoustic Variables As sound propagates, it causes mechanical changes in the medium. These changes are measurable in four physical quantities called the acoustic variables:  Pressure  Density  Temperature  Particle motion (distance)

18. Pegasus Lectures, Inc. COPYRIGHT 2006 The Sound Classification Tree Fig. 9: (Pg 88)

19. Pegasus Lectures, Inc. COPYRIGHT 2006 Units of Pressure There are many different units commonly used to measure pressure such as:  Atmospheres  mmHg  Pascals  Kg/m 2  Lbs/in 2  Dynes/cm 2

20. Pegasus Lectures, Inc. COPYRIGHT 2006 Equation for Density The concept of density is very important in ultrasound. Density is defined as mass per volume or: (Pg 89)

21. Pegasus Lectures, Inc. COPYRIGHT 2006 Wave Characteristics As sound propagates, it causes mechanical changes in the medium

22. Pegasus Lectures, Inc. COPYRIGHT 2006 Frequency of Sound Frequency is how many times an event occurs per time. For sound, the frequency refers to how many cycles of compression and rarefaction occur per second. 123 3 cycles /second = 3 Hz Wave Propagation

23. Pegasus Lectures, Inc. COPYRIGHT 2006 Frequency of a Transverse Wave For a transverse wave, the frequency is the number of cycles of maxima and minima. We usually draw a sound wave as transverse since it is easier to draw. 123456 6 cycles /second = 6 Hz

24. Pegasus Lectures, Inc. COPYRIGHT 2006 Graphical Depiction of a 2 Hz wave Fig. 10: (Pg 93)

25. Pegasus Lectures, Inc. COPYRIGHT 2006 Transverse Depiction of a 4 Hz Wave Fig. 11: (Pg 94)

26. Pegasus Lectures, Inc. COPYRIGHT 2006 Interpreting the Period Fig. 12: Depiction of the Period as the Reciprocal of the Frequency (Pg 95) Frequency and Time are always Reciprocals

27. Pegasus Lectures, Inc. COPYRIGHT 2006 Period of Sound (P or T) The period is the time it takes for the wave to transition from compression through rarefaction and back to compression. Note that the period and the frequency are reciprocals 123 3 cycles /second = 3 Hz Wave Propagation 1/3 second

28. Pegasus Lectures, Inc. COPYRIGHT 2006 Frequency and Period The frequency and the period give the same information. You should be able to convert back and forth between the period and the frequency.  Frequency = 2 Hz  Period = 1/(2 Hz) = 0.5 sec  Frequency = 10 Hz  Period = 1/(10 Hz) = 0.1 sec  Frequency = 1 kHz  Period = 1/(1 kHz) = 1 msec  Frequency = 2 MHz  Period = 1/(2 MHz) = 0.5  sec  Period = 0.1 msec  frequency = 1/(0.1 msec) = 10 kHz

29. Pegasus Lectures, Inc. COPYRIGHT 2006 Propagation Velocity (c) The propagation velocity of sound is the distance sound can travel per unit of time.  Units are distance per time such as m/sec.  The propagation velocity is also sometimes referred to as the propagation speed.  The propagation velocity depends on the physical properties of the medium (the material through which the sound is traveling) and is not dependent on the frequency of the sound wave.  Sound travels much faster in water than in air.  Sound travels slightly faster in tissue than in water.  Sound travels much faster in bone than in tissue.

30. Pegasus Lectures, Inc. COPYRIGHT 2006 Depicting the Velocity In this example, the train moves 11 meters in 10 seconds, so the velocity is 1.1 m/sec. Fig. 13: (Pg 96)

31. Pegasus Lectures, Inc. COPYRIGHT 2006 Depicting Propagation Velocity In this case, the sound has traveled a total distance of 1540 meters in a time period of 1 sec, so the propagation velocity is 1540 m/sec. Fig. 14: (Pg 96)

32. Pegasus Lectures, Inc. COPYRIGHT 2006 Different Frequencies Same Propagation Speed Fig. 15: (Pg 97)

33. Pegasus Lectures, Inc. COPYRIGHT 2006 Different Frequencies Same Propagation Speed (Animation) (Pg 98 A)

34. Pegasus Lectures, Inc. COPYRIGHT 2006 Same Frequency but Different Propagation Speeds Fig. 16: (Pg 98)

35. Pegasus Lectures, Inc. COPYRIGHT 2006 Wavelength ( ) The wavelength for a sound wave is the physical distance from one compression to the next compression. Transverse Wave Wave Propagation Longitudinal Wave

36. Pegasus Lectures, Inc. COPYRIGHT 2006 Same Frequency but Different Propagation Speeds (Animation) (Pg 98 B)

37. Pegasus Lectures, Inc. COPYRIGHT 2006 Depicting Wavelength Fig. 17: Longer Wavelength (Pg 99) Fig. 18: Shorter Wavelength (Pg 99)

38. Pegasus Lectures, Inc. COPYRIGHT 2006 Distinguishing Wavelength From Period (Animation) Pg. 99

39. Pegasus Lectures, Inc. COPYRIGHT 2006 Parameters That Affect the Wavelength Recall that the frequency of a wave is determined by the source of the wave. The propagation velocity of a wave is determined by the properties of the medium. The wavelength is affected by both the frequency and the propagation velocity.

40. Pegasus Lectures, Inc. COPYRIGHT 2006 Effect of Propagation Velocity on Wavelength Fig. 20: (Page 99)

41. Pegasus Lectures, Inc. COPYRIGHT 2006 Effect of Propagation Velocity on Wavelength Fig. 20: (Page 99)

42. Pegasus Lectures, Inc. COPYRIGHT 2006 Effect of Frequency on Wavelength Fig. 21: (Pg 101)

43. Pegasus Lectures, Inc. COPYRIGHT 2006 Wavelength Equation The wavelength of a sound wave depends on both the frequency and the propagation speed. A higher propagation speed “stretches” out the wave. A lower frequency “stretches” out the wave.

44. Pegasus Lectures, Inc. COPYRIGHT 2006 Amplitude Fig. 22: Measuring the Amplitude (Pg 102) Amplitude is a measure of how “big” or “strong”. Formally, amplitude is defined as the maximum variation of a variable from its mean value.

45. Pegasus Lectures, Inc. COPYRIGHT 2006 Developing the Amplitude Equation Fig. 23: (Pg 103) The amplitude is determined by measuring the difference between the mean and the maximum.

46. Pegasus Lectures, Inc. COPYRIGHT 2006 Amplitude Equation (continued) Fig. 25: (Pg 104) The amplitude can also be determined by measuring half the difference between the minimum and the maximum.

47. Pegasus Lectures, Inc. COPYRIGHT 2006 Amplitude Equation (continued) Fig. 24: (Pg 103) The amplitude can also be determined by measuring the difference between the mean and the minimum.

48. Pegasus Lectures, Inc. COPYRIGHT 2006 Amplitude Summary Definition: The maximum variation of a variable from its mean. Equation: Amplitude = Max – Mean = Mean – Min = (Max – Min)/2 Mean Maximum Minimum

49. Pegasus Lectures, Inc. COPYRIGHT 2006 Notes